Richard Young Richard Young Optronic Laboratories Kathleen Muray Kathleen Muray INPHORA Carolyn Jones Carolyn Jones CJ Enterprises

CIE 2CIE 2ndnd Expert Symposium on LEDs Expert Symposium on LEDs

Quantifying Quantifying

Photometric Spectral Photometric Spectral

Mismatch Uncertainties Mismatch Uncertainties

in LED Measurementsin LED Measurements

Quantifying Quantifying

Photometric Spectral Photometric Spectral

Mismatch Uncertainties Mismatch Uncertainties

in LED Measurementsin LED Measurements

Richard Young Richard Young Optronic Laboratories

Kathleen Muray Kathleen Muray INPHORA

Carolyn Jones Carolyn Jones CJ Enterprises

Richard Young Richard Young Optronic Laboratories

Kathleen Muray Kathleen Muray INPHORA

Carolyn Jones Carolyn Jones CJ Enterprises


IntroductionIntroductionPhotometer relative responses

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Wavelength [nm]

Rel

ativ

e re

spo

nse

Photopic

Photometer 1

Photometer 2

Photometer 3

Ideally, Ideally, photometer photometer response response

should match should match the photopic the photopic

curvecurve

Ideally, Ideally, photometer photometer response response

should match should match the photopic the photopic

curvecurve

We can see mis-We can see mis-matches at low matches at low response better response better on a logarithmic on a logarithmic

plot.plot.

We can see mis-We can see mis-matches at low matches at low response better response better on a logarithmic on a logarithmic

plot.plot.



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Wavelength [nm]

Re

lati

ve

re

sp

on

se

Photopic

Photometer 1

Photometer 2

Photometer 3

They often They often deviate in the deviate in the

BlueBlue

They often They often deviate in the deviate in the

BlueBlue

Photometers use Photometers use filter/detector filter/detector

combinations to combinations to approximate photopic approximate photopic

responseresponse

Photometers use Photometers use filter/detector filter/detector

combinations to combinations to approximate photopic approximate photopic

responseresponse

This approximation can This approximation can sometimes be quite good, sometimes be quite good,

but is never perfect.but is never perfect.

This approximation can This approximation can sometimes be quite good, sometimes be quite good,

but is never perfect.but is never perfect.

And in And in the Redthe RedAnd in And in

the Redthe Red

The highest The highest response and response and

best fit are best fit are normally normally

around 555 nmaround 555 nm

The highest The highest response and response and

best fit are best fit are normally normally

around 555 nmaround 555 nmThis plot shows 3 This plot shows 3 photometers.photometers.

This plot shows 3 This plot shows 3 photometers.photometers.

Photometer 1Photometer 1Photometer 1Photometer 1Photometer 2Photometer 2Photometer 2Photometer 2Photometer 3Photometer 3Photometer 3Photometer 3


IntroductionIntroduction

If the photometer is calibrated with a white If the photometer is calibrated with a white light source, such as illuminant A:light source, such as illuminant A: Correct measurements will only be made if Correct measurements will only be made if

the test source is also illuminant A.the test source is also illuminant A.The errors in measuring other sources The errors in measuring other sources

depend on:depend on: The accuracy of matching the photometer The accuracy of matching the photometer

response to the photopic curve.response to the photopic curve. The difference between the test source and The difference between the test source and

illuminant A.illuminant A.

If the photometer is calibrated with a white If the photometer is calibrated with a white light source, such as illuminant A:light source, such as illuminant A: Correct measurements will only be made if Correct measurements will only be made if

the test source is also illuminant A.the test source is also illuminant A.The errors in measuring other sources The errors in measuring other sources

depend on:depend on: The accuracy of matching the photometer The accuracy of matching the photometer

response to the photopic curve.response to the photopic curve. The difference between the test source and The difference between the test source and

illuminant A.illuminant A.



If the photometer response is very close to If the photometer response is very close to photopic:photopic: There is little error, relaxing the need for There is little error, relaxing the need for

similarity between calibration and test similarity between calibration and test sources.sources.

If the test source is very close to illuminant If the test source is very close to illuminant A:A: There will be little error, relaxing the There will be little error, relaxing the

accuracy requirements of the photometer accuracy requirements of the photometer response.response.

If the photometer response is very close to If the photometer response is very close to photopic:photopic: There is little error, relaxing the need for There is little error, relaxing the need for

similarity between calibration and test similarity between calibration and test sources.sources.

If the test source is very close to illuminant If the test source is very close to illuminant A:A: There will be little error, relaxing the There will be little error, relaxing the

accuracy requirements of the photometer accuracy requirements of the photometer response.response.



However, an LED is so different from However, an LED is so different from illuminant A that the photometer needs to illuminant A that the photometer needs to match the photopic response curve match the photopic response curve veryvery closely.closely.

A “goodness of fit” parameter, fA “goodness of fit” parameter, f11’, has ’, has been used for many years as the selection been used for many years as the selection parameter for photometers.parameter for photometers. It is intended to apply to white light sources It is intended to apply to white light sources

and DOES NOT WORK for LEDs (with the and DOES NOT WORK for LEDs (with the possible exception of white LEDs).possible exception of white LEDs).

However, an LED is so different from However, an LED is so different from illuminant A that the photometer needs to illuminant A that the photometer needs to match the photopic response curve match the photopic response curve veryvery closely.closely.

A “goodness of fit” parameter, fA “goodness of fit” parameter, f11’, has ’, has been used for many years as the selection been used for many years as the selection parameter for photometers.parameter for photometers. It is intended to apply to white light sources It is intended to apply to white light sources

and DOES NOT WORK for LEDs (with the and DOES NOT WORK for LEDs (with the possible exception of white LEDs).possible exception of white LEDs).



To remind you how fTo remind you how f11’ is defined:’ is defined:To remind you how fTo remind you how f11’ is defined:’ is defined:

0

0

*

'

dV

dVs

= frel

1

Where:Where:Where:Where:

)s(

d )s( S

d )V( S = rel

0relA,

0

A,

rel

)(s*

Illuminant AIlluminant AIlluminant AIlluminant A

Publication CIE 69-1987: Methods of Publication CIE 69-1987: Methods of characterizing illuminance meters and characterizing illuminance meters and

luminance meters: Performance, luminance meters: Performance, characteristics and specificationscharacteristics and specifications

Publication CIE 69-1987: Methods of Publication CIE 69-1987: Methods of characterizing illuminance meters and characterizing illuminance meters and

luminance meters: Performance, luminance meters: Performance, characteristics and specificationscharacteristics and specifications

The calculation requires The calculation requires the photometer relative the photometer relative

response.response.

The calculation requires The calculation requires the photometer relative the photometer relative

response.response.



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Wavelength [nm]

Re

lati

ve

re

sp

on

se

Photopic

Photometer 1

Photometer 2

Photometer 3

LEDs are generally LEDs are generally narrow band, and are very narrow band, and are very

unlike illuminant Aunlike illuminant A

LEDs are generally LEDs are generally narrow band, and are very narrow band, and are very

unlike illuminant Aunlike illuminant A

Measurements of LEDs Measurements of LEDs can therefore have large can therefore have large errors associated with errors associated with white light calibrations.white light calibrations.

Measurements of LEDs Measurements of LEDs can therefore have large can therefore have large errors associated with errors associated with white light calibrations.white light calibrations.

Especially in Especially in the Bluethe Blue

Especially in Especially in the Bluethe Blue

And in And in the Redthe RedAnd in And in

the Redthe Red



If the relative spectral distribution of the If the relative spectral distribution of the LED LED andand photometer response are known, photometer response are known, the measured photopic value can be the measured photopic value can be corrected for the difference between the corrected for the difference between the calibration source and the LED.calibration source and the LED. This is called the spectral mismatch This is called the spectral mismatch

correction factor, F (also known as color correction factor, F (also known as color correction factor in some older documents).correction factor in some older documents).

When the calibration source is illuminant A, When the calibration source is illuminant A, the spectral mismatch factor is given the the spectral mismatch factor is given the symbol F*.symbol F*.

If the relative spectral distribution of the If the relative spectral distribution of the LED LED andand photometer response are known, photometer response are known, the measured photopic value can be the measured photopic value can be corrected for the difference between the corrected for the difference between the calibration source and the LED.calibration source and the LED. This is called the spectral mismatch This is called the spectral mismatch

correction factor, F (also known as color correction factor, F (also known as color correction factor in some older documents).correction factor in some older documents).

When the calibration source is illuminant A, When the calibration source is illuminant A, the spectral mismatch factor is given the the spectral mismatch factor is given the symbol F*.symbol F*.


Spectral Mismatch FactorsSpectral Mismatch FactorsLED relative spectral distributions

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Wavelength [nm]

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lati

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ten

sit

y

Here are the spectral Here are the spectral distributions for a range of distributions for a range of

LEDsLEDs

Here are the spectral Here are the spectral distributions for a range of distributions for a range of

LEDsLEDs

We can therefore calculate the We can therefore calculate the spectral mismatch factors for spectral mismatch factors for

Photometer 1.Photometer 1.

We can therefore calculate the We can therefore calculate the spectral mismatch factors for spectral mismatch factors for

Photometer 1.Photometer 1.


Spectral Mismatch FactorsSpectral Mismatch FactorsF* for a photometer measuring LEDs

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LED Peak Wavelength [nm]

F*

Photometer 1

IDEAL

Actual LEDs

LED measurements using this LED measurements using this photometer, can be multiplied photometer, can be multiplied by the appropriate F* to give by the appropriate F* to give

corrected results.corrected results.

LED measurements using this LED measurements using this photometer, can be multiplied photometer, can be multiplied by the appropriate F* to give by the appropriate F* to give

corrected results.corrected results.


Spectral Mismatch FactorsSpectral Mismatch Factors

Can we calculate the spectral mismatch Can we calculate the spectral mismatch factors without measuring a whole range factors without measuring a whole range of LEDs?of LEDs? Although spectral distributions of LEDs are Although spectral distributions of LEDs are

often asymmetric, they have a similarity of often asymmetric, they have a similarity of shape that might be reproduced by shape that might be reproduced by calculation.calculation.

To keep the calculation simple and To keep the calculation simple and relevant, it should be based on information relevant, it should be based on information readily available: peak wavelength and full-readily available: peak wavelength and full-width-at-half-maximum (FWHM).width-at-half-maximum (FWHM).

Can we calculate the spectral mismatch Can we calculate the spectral mismatch factors without measuring a whole range factors without measuring a whole range of LEDs?of LEDs? Although spectral distributions of LEDs are Although spectral distributions of LEDs are

often asymmetric, they have a similarity of often asymmetric, they have a similarity of shape that might be reproduced by shape that might be reproduced by calculation.calculation.

To keep the calculation simple and To keep the calculation simple and relevant, it should be based on information relevant, it should be based on information readily available: peak wavelength and full-readily available: peak wavelength and full-width-at-half-maximum (FWHM).width-at-half-maximum (FWHM).



Using a Gaussian curve within the FWHM Using a Gaussian curve within the FWHM limits and an exponential curve outside, limits and an exponential curve outside, the LED spectrum is represented the LED spectrum is represented reasonably well.reasonably well.

Using a Gaussian curve within the FWHM Using a Gaussian curve within the FWHM limits and an exponential curve outside, limits and an exponential curve outside, the LED spectrum is represented the LED spectrum is represented reasonably well.reasonably well.



Mathematically, for Mathematically, for LL H H

[[LL is the lower and is the lower and HH is the upper FWHM is the upper FWHM limit, limit, pp is the peak wavelength] is the peak wavelength]

Mathematically, for Mathematically, for LL H H

[[LL is the lower and is the lower and HH is the upper FWHM is the upper FWHM limit, limit, pp is the peak wavelength] is the peak wavelength]

2

25.0ln4

FWHM

p

e



For For L L and and H H > >

[[LL is the lower and is the lower and HH is the upper FWHM is the upper FWHM

limit, limit, pp is the peak wavelength] is the peak wavelength]

For For L L and and H H > >

[[LL is the lower and is the lower and HH is the upper FWHM is the upper FWHM

limit, limit, pp is the peak wavelength] is the peak wavelength]

FWHM

p

e

5.0ln4

2


F* for a photometer measuring LEDs

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F*

Photometer 1

IDEAL

Actual LEDs

So, here are the F* factors So, here are the F* factors calculated from real LED calculated from real LED

spectra again…spectra again…

So, here are the F* factors So, here are the F* factors calculated from real LED calculated from real LED

spectra again…spectra again…


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F*

Photometer 1

IDEAL

Actual LEDs

Calculated LEDs

……and here are the predicted and here are the predicted F* values using the modelled F* values using the modelled LED spectra (shown in red).LED spectra (shown in red).

……and here are the predicted and here are the predicted F* values using the modelled F* values using the modelled LED spectra (shown in red).LED spectra (shown in red).




The agreement between real and modelled The agreement between real and modelled LED spectral calculations means we can LED spectral calculations means we can express F* as a smooth curve rather than express F* as a smooth curve rather than individual points.individual points.

We don’t have to do all those LED spectral We don’t have to do all those LED spectral measurements.measurements.

We can express F* for different FWHM We can express F* for different FWHM values at each peak wavelength.values at each peak wavelength. And then something interesting happens…And then something interesting happens…

The agreement between real and modelled The agreement between real and modelled LED spectral calculations means we can LED spectral calculations means we can express F* as a smooth curve rather than express F* as a smooth curve rather than individual points.individual points.

We don’t have to do all those LED spectral We don’t have to do all those LED spectral measurements.measurements.

We can express F* for different FWHM We can express F* for different FWHM values at each peak wavelength.values at each peak wavelength. And then something interesting happens…And then something interesting happens…



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F*

Photometer 1IDEAL

20 nm FWHM

30 nm FWHM

40 nm FWHM

50 nm FWHM

70 nm FWHM

Actual LEDs

Calculated LEDs

We see that the F* curve We see that the F* curve has places where FWHM has places where FWHM

hardly mattershardly matters

We see that the F* curve We see that the F* curve has places where FWHM has places where FWHM

hardly mattershardly matters

And other places where And other places where F* changes rapidly with F* changes rapidly with

FWHMFWHM

And other places where And other places where F* changes rapidly with F* changes rapidly with

FWHMFWHM

There are wavelength There are wavelength ranges where F* ranges where F* changes rapidlychanges rapidly

There are wavelength There are wavelength ranges where F* ranges where F* changes rapidlychanges rapidly

And other ranges where And other ranges where F* hardly changes at allF* hardly changes at allAnd other ranges where And other ranges where F* hardly changes at allF* hardly changes at all



LEDs differ in peak wavelength and LEDs differ in peak wavelength and FWHM, so if we want to describe how F* FWHM, so if we want to describe how F* changes for real LEDs:changes for real LEDs: We must include a wavelength componentWe must include a wavelength component We must include a FWHM componentWe must include a FWHM component

LEDs differ in peak wavelength and LEDs differ in peak wavelength and FWHM, so if we want to describe how F* FWHM, so if we want to describe how F* changes for real LEDs:changes for real LEDs: We must include a wavelength componentWe must include a wavelength component We must include a FWHM componentWe must include a FWHM component



The mathematical model for the LED The mathematical model for the LED spectra works for this photometer, but spectra works for this photometer, but does it work for all?does it work for all?

The mathematical model for the LED The mathematical model for the LED spectra works for this photometer, but spectra works for this photometer, but does it work for all?does it work for all?



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F*

Photometer 2IDEAL

20 nm FWHM

30 nm FWHM

40 nm FWHM

50 nm FWHM

70 nm FWHM

Actual LEDs

Calculated LEDs

It seems to work even better It seems to work even better for Photometer 2 than it did for Photometer 2 than it did

for Photometer 1.for Photometer 1.

It seems to work even better It seems to work even better for Photometer 2 than it did for Photometer 2 than it did

for Photometer 1.for Photometer 1.



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F*

Photometer 3IDEAL

20 nm FWHM

30 nm FWHM

40 nm FWHM

50 nm FWHM

70 nm FWHM

Actual LEDs

Calculated LEDs


Photometer 3 Photometer 3 shows some shows some

differences as the differences as the F* value increasesF* value increases

Photometer 3 Photometer 3 shows some shows some

differences as the differences as the F* value increasesF* value increases

This is because the mathematical This is because the mathematical model is symmetric and the LED model is symmetric and the LED spectrum is not. These LEDs are spectrum is not. These LEDs are

narrow band and highly narrow band and highly asymmetric, combined with a asymmetric, combined with a

poor photopic fit of the detectorpoor photopic fit of the detector

This is because the mathematical This is because the mathematical model is symmetric and the LED model is symmetric and the LED spectrum is not. These LEDs are spectrum is not. These LEDs are

narrow band and highly narrow band and highly asymmetric, combined with a asymmetric, combined with a

poor photopic fit of the detectorpoor photopic fit of the detector

However, it still matches the However, it still matches the general shape of the F* curve, general shape of the F* curve,

which is all that is required in this which is all that is required in this paper.paper.

However, it still matches the However, it still matches the general shape of the F* curve, general shape of the F* curve,

which is all that is required in this which is all that is required in this paper.paper.



The point of this presentation is not to replace The point of this presentation is not to replace LED spectral measurement in the calculation of LED spectral measurement in the calculation of spectral mismatch factors.spectral mismatch factors. Though it seems to do a good job of this.Though it seems to do a good job of this.

The point is, when testing LEDs in a production The point is, when testing LEDs in a production environment, there are small changes in peak environment, there are small changes in peak wavelength and FWHM between devices of the wavelength and FWHM between devices of the same type.same type. And measuring the spectrum, or even peak And measuring the spectrum, or even peak

wavelength, to get a new F* for each device is not wavelength, to get a new F* for each device is not practical.practical.

The point of this presentation is not to replace The point of this presentation is not to replace LED spectral measurement in the calculation of LED spectral measurement in the calculation of spectral mismatch factors.spectral mismatch factors. Though it seems to do a good job of this.Though it seems to do a good job of this.

The point is, when testing LEDs in a production The point is, when testing LEDs in a production environment, there are small changes in peak environment, there are small changes in peak wavelength and FWHM between devices of the wavelength and FWHM between devices of the same type.same type. And measuring the spectrum, or even peak And measuring the spectrum, or even peak

wavelength, to get a new F* for each device is not wavelength, to get a new F* for each device is not practical.practical.



At this point it is worth noting that if a calibrated At this point it is worth noting that if a calibrated LED is used to calibrate the photometer rather LED is used to calibrate the photometer rather than a white light source, the photometer will than a white light source, the photometer will already read correctly for that LED.already read correctly for that LED. It is equivalent to calibrating It is equivalent to calibrating andand applying the F* applying the F*

factor in one process.factor in one process.

All other LEDs will still need a spectral mismatch All other LEDs will still need a spectral mismatch factor, F, to correct the measurement result.factor, F, to correct the measurement result. And that includes the production devices.And that includes the production devices.

At this point it is worth noting that if a calibrated At this point it is worth noting that if a calibrated LED is used to calibrate the photometer rather LED is used to calibrate the photometer rather than a white light source, the photometer will than a white light source, the photometer will already read correctly for that LED.already read correctly for that LED. It is equivalent to calibrating It is equivalent to calibrating andand applying the F* applying the F*

factor in one process.factor in one process.

All other LEDs will still need a spectral mismatch All other LEDs will still need a spectral mismatch factor, F, to correct the measurement result.factor, F, to correct the measurement result. And that includes the production devices.And that includes the production devices.



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F*

Photometer 3

IDEAL

20 nm FWHM

30 nm FWHM

40 nm FWHM

50 nm FWHM

70 nm FWHM

Let us take a closer Let us take a closer look at some of these look at some of these

F* values.F* values.

Let us take a closer Let us take a closer look at some of these look at some of these

F* values.F* values.

MagnifyMagnifyMagnifyMagnify



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430 435 440 445 450 455 460 465 470 475 480


F*

Photometer 3

IDEAL

20 nm FWHM

30 nm FWHM

40 nm FWHM

50 nm FWHM

70 nm FWHM


When we apply the F* When we apply the F* factor, we are effectively factor, we are effectively

offsetting the curve at offsetting the curve at one wavelengthone wavelength

When we apply the F* When we apply the F* factor, we are effectively factor, we are effectively

offsetting the curve at offsetting the curve at one wavelengthone wavelength

This means that This means that measurements of LEDs measurements of LEDs

that have a slightly that have a slightly different wavelength still different wavelength still have an associated errorhave an associated error

This means that This means that measurements of LEDs measurements of LEDs

that have a slightly that have a slightly different wavelength still different wavelength still have an associated errorhave an associated error

The size of the error The size of the error depends on how different depends on how different

the wavelength is and the wavelength is and how quickly the F* factor how quickly the F* factor changes in that region.changes in that region.

The size of the error The size of the error depends on how different depends on how different

the wavelength is and the wavelength is and how quickly the F* factor how quickly the F* factor changes in that region.changes in that region.


ffLEDLED

We can define a “goodness of fit” We can define a “goodness of fit” parameter, like fparameter, like f11’ but specifically applying ’ but specifically applying

to LEDs – fto LEDs – fLEDLED..

The fThe fLED LED parameter is “the average absolute parameter is “the average absolute

spectral mismatch error over a wavelength spectral mismatch error over a wavelength region relative to the central wavelength of region relative to the central wavelength of that region.”that region.”

We can define a “goodness of fit” We can define a “goodness of fit” parameter, like fparameter, like f11’ but specifically applying ’ but specifically applying

to LEDs – fto LEDs – fLEDLED..

The fThe fLED LED parameter is “the average absolute parameter is “the average absolute

spectral mismatch error over a wavelength spectral mismatch error over a wavelength region relative to the central wavelength of region relative to the central wavelength of that region.”that region.”

NOTE: It is NOTE: It is NOTNOT a correction factor to a correction factor to be applied, but it be applied, but it ISIS an indicator of the an indicator of the

suitability and quality of the suitability and quality of the photometer for measurement of any photometer for measurement of any

single color LED.single color LED.

NOTE: It is NOTE: It is NOTNOT a correction factor to a correction factor to be applied, but it be applied, but it ISIS an indicator of the an indicator of the

suitability and quality of the suitability and quality of the photometer for measurement of any photometer for measurement of any

single color LED.single color LED.


ffLEDLED

There is one value of fThere is one value of fLEDLED for each for each wavelength and FWHM, but because we can wavelength and FWHM, but because we can effectively model the LED spectral effectively model the LED spectral distribution, it can be easily calculated from distribution, it can be easily calculated from the photometer response.the photometer response.

ffLEDLED has two components. has two components. Errors introduced by measuring LEDs at Errors introduced by measuring LEDs at

different wavelengths to the calibration –wdifferent wavelengths to the calibration –wLEDLED.. Errors introduced by measuring LEDs at Errors introduced by measuring LEDs at

different FWHMs to the calibration – hdifferent FWHMs to the calibration – hLEDLED..

There is one value of fThere is one value of fLEDLED for each for each wavelength and FWHM, but because we can wavelength and FWHM, but because we can effectively model the LED spectral effectively model the LED spectral distribution, it can be easily calculated from distribution, it can be easily calculated from the photometer response.the photometer response.

ffLEDLED has two components. has two components. Errors introduced by measuring LEDs at Errors introduced by measuring LEDs at

different wavelengths to the calibration –wdifferent wavelengths to the calibration –wLEDLED.. Errors introduced by measuring LEDs at Errors introduced by measuring LEDs at

different FWHMs to the calibration – hdifferent FWHMs to the calibration – hLEDLED..


wwLEDLED

Mathematically, the F* value for an LED at Mathematically, the F* value for an LED at the central wavelength, c, is:the central wavelength, c, is: Where Where s(s()) is the photometer response and is the photometer response and SScc

LEDLED(() is the LED spectral distribution.) is the LED spectral distribution.

Mathematically, the F* value for an LED at Mathematically, the F* value for an LED at the central wavelength, c, is:the central wavelength, c, is: Where Where s(s()) is the photometer response and is the photometer response and SScc


dsSdVS

dVSdsSF

LEDcA

LEDcA

c..

..*


wwLEDLED

Similarly, the F* value for an LED at some Similarly, the F* value for an LED at some other wavelength, p, is:other wavelength, p, is: Where Where s(s()) is the photometer response and is the photometer response and SSpp


Similarly, the F* value for an LED at some Similarly, the F* value for an LED at some other wavelength, p, is:other wavelength, p, is: Where Where s(s()) is the photometer response and is the photometer response and SSpp


dsSdVS

dVSdsSF

LEDpA

LEDpA

p..

..*


The error when measuring an LED at The error when measuring an LED at wavelength p using the Fwavelength p using the Fcc* value at * value at

wavelength c is:wavelength c is:

The error when measuring an LED at The error when measuring an LED at wavelength p using the Fwavelength p using the Fcc* value at * value at

wavelength c is:wavelength c is:

NOTE: This equation no longer contains a reference to NOTE: This equation no longer contains a reference to the calibration source, so it does not matter if it was the calibration source, so it does not matter if it was

calibrated with white light or a calibrated LED.calibrated with white light or a calibrated LED.

p,cp,c depends only on the photometer and the LED depends only on the photometer and the LED

spectral distributions. If the modelled spectral spectral distributions. If the modelled spectral distributions are used, it is purely a photometer distributions are used, it is purely a photometer

characteristic.characteristic.

NOTE: This equation no longer contains a reference to NOTE: This equation no longer contains a reference to the calibration source, so it does not matter if it was the calibration source, so it does not matter if it was

calibrated with white light or a calibrated LED.calibrated with white light or a calibrated LED.

p,cp,c depends only on the photometer and the LED depends only on the photometer and the LED

spectral distributions. If the modelled spectral spectral distributions. If the modelled spectral distributions are used, it is purely a photometer distributions are used, it is purely a photometer

characteristic.characteristic.

dsSdVS

dVSdsSLEDp

LEDc

LEDp

LEDc

cp..

..1,

wwLEDLED

*

*1,

c

pcp F

F


wwLEDLED

Recall the definition of fRecall the definition of fLEDLED:: ““the average absolute spectral mismatch the average absolute spectral mismatch

error over a wavelength region relative to error over a wavelength region relative to the central wavelength of that region.”the central wavelength of that region.”

We can now define wWe can now define wLEDLED in mathematical in mathematical

terms:terms:

Recall the definition of fRecall the definition of fLEDLED:: ““the average absolute spectral mismatch the average absolute spectral mismatch

error over a wavelength region relative to error over a wavelength region relative to the central wavelength of that region.”the central wavelength of that region.”

We can now define wWe can now define wLEDLED in mathematical in mathematical

terms:terms:

12

.

)(

2

1

,

pp

dp

cw

p

p

cp

LED

Where p1 and p2 Where p1 and p2 are the are the

wavelength wavelength limits of the limits of the

regionregion

Where p1 and p2 Where p1 and p2 are the are the

wavelength wavelength limits of the limits of the

regionregion


wwLEDLED

So wSo wLEDLED can be calculated for any central can be calculated for any central

wavelength and FWHM.wavelength and FWHM. It should be shown as wIt should be shown as wLEDLED(c,FWHM) to reflect (c,FWHM) to reflect

this.this. Since it is independent of calibration source, a Since it is independent of calibration source, a

full photometer response curve is not required.full photometer response curve is not required. 3 FWHMs around the central wavelength should 3 FWHMs around the central wavelength should

be sufficient.be sufficient.

The photometer response The photometer response doesdoes need to be done need to be done at 1nm intervals or smaller for good results.at 1nm intervals or smaller for good results.

So wSo wLEDLED can be calculated for any central can be calculated for any central

wavelength and FWHM.wavelength and FWHM. It should be shown as wIt should be shown as wLEDLED(c,FWHM) to reflect (c,FWHM) to reflect

this.this. Since it is independent of calibration source, a Since it is independent of calibration source, a

full photometer response curve is not required.full photometer response curve is not required. 3 FWHMs around the central wavelength should 3 FWHMs around the central wavelength should

be sufficient.be sufficient.

The photometer response The photometer response doesdoes need to be done need to be done at 1nm intervals or smaller for good results.at 1nm intervals or smaller for good results.


wwLEDLED

We still need to define the wavelength We still need to define the wavelength “region” in order to calculate “region” in order to calculate wwLEDLED(c,FWHM).(c,FWHM).

Based on data for over 900 LEDs in 63 Based on data for over 900 LEDs in 63 batches, covering most of the visible batches, covering most of the visible range, we propose range, we propose ± 5 nm around the ± 5 nm around the central wavelength.central wavelength.

We still need to define the wavelength We still need to define the wavelength “region” in order to calculate “region” in order to calculate wwLEDLED(c,FWHM).(c,FWHM).

Based on data for over 900 LEDs in 63 Based on data for over 900 LEDs in 63 batches, covering most of the visible batches, covering most of the visible range, we propose range, we propose ± 5 nm around the ± 5 nm around the central wavelength.central wavelength.


wwLEDLED4

30

44

0

45

0

46

0

47

0

48

0

49

0

50

0

51

0

52

0

53

0

54

0

55

0

56

0

57

0

58

0

59

0

60

0

61

0

62

0

63

0

64

0

65

0

66

0-5 -4 -3 -2 -1 0 1 2 3 4 5

-11%-10%-9%-8%-7%-6%-5%-4%-3%-2%-1%0%1%2%3%4%5%6%7%8%9%10%

p,c

CentralWavelength [nm]

c-p

-11%--10% -10%--9% -9%--8% -8%--7%-7%--6% -6%--5% -5%--4% -4%--3%-3%--2% -2%--1% -1%-0% 0%-1%1%-2% 2%-3% 3%-4% 4%-5%5%-6% 6%-7% 7%-8% 8%-9%9%-10%

The first stage is to calculate The first stage is to calculate p,cp,c

over the region.over the region.The first stage is to calculate The first stage is to calculate p,cp,c

over the region.over the region.

This is the result This is the result for photometer 1 for photometer 1 at 20 nm FWHM.at 20 nm FWHM.

This is the result This is the result for photometer 1 for photometer 1 at 20 nm FWHM.at 20 nm FWHM.


wLED values for photometer 1 vs central wavelength & FWHM

0%

1%

2%

3%

4%

5%

6%

7%

400 450 500 550 600 650

Central Wavelength [nm]

wLE

D

10 nm

15 nm

20 nm

25 nm

30 nm

35 nm

40 nm

45 nm

50 nm

55 nm

60 nm

65 nm

70 nm

wwLEDLED

The next stage is to The next stage is to calculate wcalculate wLEDLED values. values.The next stage is to The next stage is to

calculate wcalculate wLEDLED values. values.

These results These results show that wshow that wLEDLED

varies strongly varies strongly with FWHM.with FWHM.

These results These results show that wshow that wLEDLED

varies strongly varies strongly with FWHM.with FWHM.


Using similar reasoning to wUsing similar reasoning to wLEDLED

calculationscalculations The error when measuring an LED at FWHM The error when measuring an LED at FWHM

h using the Fh using the FHH* value at FWHM H, both at * value at FWHM H, both at peak wavelength c is:peak wavelength c is:

Using similar reasoning to wUsing similar reasoning to wLEDLED

calculationscalculations The error when measuring an LED at FWHM The error when measuring an LED at FWHM

h using the Fh using the FHH* value at FWHM H, both at * value at FWHM H, both at peak wavelength c is:peak wavelength c is:

dsSdVS

dVSdsSLED

hcLED

Hc

LEDhc

LEDHc

Hh..

..1

,,

,,

,

hhLEDLED

*

*1

,

,,

Hc

hcHh F

F


hhLEDLED

We can define hWe can define hLEDLED in similar mathematical in similar mathematical

terms to wterms to wLEDLED::

We can define hWe can define hLEDLED in similar mathematical in similar mathematical

terms to wterms to wLEDLED::

12

.

),(

2

1

,

hh

dh

Hch

h

h

Hh

LED

Where h1 and h2 Where h1 and h2 are are ± 5 nm limits ± 5 nm limits

around the around the central FWHM central FWHM

value, Hvalue, H

Where h1 and h2 Where h1 and h2 are are ± 5 nm limits ± 5 nm limits

around the around the central FWHM central FWHM

value, Hvalue, H


hhLEDLEDhLED values for photometer 1 vs central wavelength & FWHM

0%

1%

2%

3%

4%

5%

6%

400 450 500 550 600 650

Region central wavelength [nm]

fLE

D

10 nm

15 nm

20 nm

25 nm

30 nm

35 nm

40 nm

45 nm

50 nm

55 nm

60 nm

65 nm

70 nm

Like wLike wLEDLED, h, hLEDLED is is

strongly dependent strongly dependent on FWHM.on FWHM.

Like wLike wLEDLED, h, hLEDLED is is

strongly dependent strongly dependent on FWHM.on FWHM.


hhLEDLED

So now we have the two components:So now we have the two components: wwLEDLED(c,H) gives the error for peak (c,H) gives the error for peak

wavelength change.wavelength change. hhLED LED (c,H) gives the error for FWHM change.(c,H) gives the error for FWHM change.

We can combine them to give the general We can combine them to give the general error indicator, ferror indicator, fLEDLED(c,H):(c,H):

So now we have the two components:So now we have the two components: wwLEDLED(c,H) gives the error for peak (c,H) gives the error for peak

wavelength change.wavelength change. hhLED LED (c,H) gives the error for FWHM change.(c,H) gives the error for FWHM change.

We can combine them to give the general We can combine them to give the general error indicator, ferror indicator, fLEDLED(c,H):(c,H):

5.022 ,,, HchHcwHcf LEDLEDLED


ffLEDLEDComponents of fLED for photometer 1 at 20 nm FWHM

0%

1%

2%

3%

4%

5%

6%

7%

8%

400 450 500 550 600 650

Wavelength [nm]

wLE

D o

r h

LED o

r f L

ED

wLED

Components of fLED for photometer 1 at 20 nm FWHM

0%

1%

2%

3%

4%

5%

6%

7%

8%

400 450 500 550 600 650

Wavelength [nm]

wLE

D o

r h

LED o

r f L

ED

hLED

Components of fLED for photometer 1 at 20 nm FWHM

0%

1%

2%

3%

4%

5%

6%

7%

8%

400 450 500 550 600 650

Wavelength [nm]

wLE

D o

r h

LED o

r f L

ED

fLED

Here is an Here is an example of wexample of wLEDLED

Here is an Here is an example of wexample of wLEDLED

We add hWe add hLEDLEDWe add hWe add hLEDLEDAnd finally fAnd finally fLED.LED.And finally fAnd finally fLED.LED.

You can see that high hYou can see that high hLEDLED is is

generally close to a low wgenerally close to a low wLED.LED.

You can see that high hYou can see that high hLEDLED is is

generally close to a low wgenerally close to a low wLED.LED.This means there are wavelengths This means there are wavelengths

where the photometer error is more where the photometer error is more sensitive to LED peak wavelength sensitive to LED peak wavelength shifts and others where it is more shifts and others where it is more

sensitive to FWHM changes.sensitive to FWHM changes.

This means there are wavelengths This means there are wavelengths where the photometer error is more where the photometer error is more sensitive to LED peak wavelength sensitive to LED peak wavelength shifts and others where it is more shifts and others where it is more

sensitive to FWHM changes.sensitive to FWHM changes.


ffLEDLED

Photometer relative responses

0.001

0.01

0.1

1

380 400 420 440 460 480 500

Wavelength [nm]

Rel

ativ

e re

spo

nse

Photopic

Photometer 1

Photometer 2

Photometer 3

This is the This is the photometer response photometer response graph shown earlier graph shown earlier

but rescaled.but rescaled.

This is the This is the photometer response photometer response graph shown earlier graph shown earlier

but rescaled.but rescaled.

Where the photometer Where the photometer response crosses the response crosses the photopic curve, their photopic curve, their

slopes are very differentslopes are very different

Where the photometer Where the photometer response crosses the response crosses the photopic curve, their photopic curve, their

slopes are very differentslopes are very different

Giving large errors with Giving large errors with wavelength changeswavelength changes

Giving large errors with Giving large errors with wavelength changeswavelength changes

But high and low But high and low contributions offset one contributions offset one another for changes in another for changes in

FWHM.FWHM.

But high and low But high and low contributions offset one contributions offset one another for changes in another for changes in

FWHM.FWHM.


ffLEDLED

ffLEDLED(c,H) values can aid in the design of (c,H) values can aid in the design of photometers.photometers. It provides instant feedback on the performance It provides instant feedback on the performance

of the photometer for LED measurements.of the photometer for LED measurements. It shows that it is the slope of the response It shows that it is the slope of the response

rather than the absolute value that is important.rather than the absolute value that is important. It does not require spectral data over the full It does not require spectral data over the full

visible region.visible region.Photometer 4, specially designed for blue Photometer 4, specially designed for blue

LEDs, can now be added to our list.LEDs, can now be added to our list.

ffLEDLED(c,H) values can aid in the design of (c,H) values can aid in the design of photometers.photometers. It provides instant feedback on the performance It provides instant feedback on the performance

of the photometer for LED measurements.of the photometer for LED measurements. It shows that it is the slope of the response It shows that it is the slope of the response

rather than the absolute value that is important.rather than the absolute value that is important. It does not require spectral data over the full It does not require spectral data over the full

visible region.visible region.Photometer 4, specially designed for blue Photometer 4, specially designed for blue

LEDs, can now be added to our list.LEDs, can now be added to our list.


ffLEDLEDComparison of Photometers at 20 nm FWHM

0%

1%

2%

3%

4%

5%

6%

7%

8%

400 450 500 550 600 650

Wavelength, c [nm]

f LE

D(c

,20)

Photometer 1

Photometer 2

Photometer 3

Photometer 4

Photometer 4 is Photometer 4 is confirmed as confirmed as

generally the best generally the best for blue LEDS.for blue LEDS.

Photometer 4 is Photometer 4 is confirmed as confirmed as

generally the best generally the best for blue LEDS.for blue LEDS.

But photometer 1 But photometer 1 is best at 430 nm.is best at 430 nm.But photometer 1 But photometer 1 is best at 430 nm.is best at 430 nm.


Comparison of Photometers at 40 nm FWHM

0%

1%

2%

3%

4%

400 450 500 550 600 650

Wavelength, c [nm]

f LE

D(c

,40)

Photometer 1

Photometer 2

Photometer 3

Photometer 4

ffLEDLED

At 40 nm FWHM At 40 nm FWHM Photometer 4 is the Photometer 4 is the best for blue LEDS best for blue LEDS

even at 430 nmeven at 430 nm

At 40 nm FWHM At 40 nm FWHM Photometer 4 is the Photometer 4 is the best for blue LEDS best for blue LEDS

even at 430 nmeven at 430 nm

Photometer 3 Photometer 3 is the worstis the worst

Photometer 3 Photometer 3 is the worstis the worstValues of fValues of fLEDLED(c,H) (c,H)

show the suitability show the suitability for LED measurement, for LED measurement, but bear no relation to but bear no relation to

the fthe f11’ value.’ value.

Values of fValues of fLEDLED(c,H) (c,H)

show the suitability show the suitability for LED measurement, for LED measurement, but bear no relation to but bear no relation to

the fthe f11’ value.’ value.

Photometer 2: fPhotometer 2: f11’ = 1.98%’ = 1.98%Photometer 2: fPhotometer 2: f11’ = 1.98%’ = 1.98%




430

460

490

520

550

580

610

64010 nm

20 nm

30 nm

40 nm

50 nm

60 nm

70 nm

0.0%0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%4.5%5.0%5.5%6.0%6.5%7.0%7.5%8.0%

f LE

D(c

,H)

Wavelength, c [nm]

FWHM, H [nm]

fLED(c,H) for photometer 1

7.50%-8.00%7.00%-7.50%6.50%-7.00%6.00%-6.50%5.50%-6.00%5.00%-5.50%4.50%-5.00%4.00%-4.50%3.50%-4.00%3.00%-3.50%2.50%-3.00%2.00%-2.50%1.50%-2.00%1.00%-1.50%0.50%-1.00%0.00%-0.50%

ffLEDLED

A 3-D plot A 3-D plot shows the shows the

variations of variations of ffLEDLED(c,H). The (c,H). The

value is color value is color coded to show coded to show

iso-value iso-value lines. Seen lines. Seen from above, from above,

this is a map.this is a map.

A 3-D plot A 3-D plot shows the shows the

variations of variations of ffLEDLED(c,H). The (c,H). The

value is color value is color coded to show coded to show

iso-value iso-value lines. Seen lines. Seen from above, from above,

this is a map.this is a map.

CIE 2CIE 2ndnd Expert Symposium on LEDs Expert Symposium on LEDs430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650

10 nm

15 nm

20 nm

25 nm

30 nm

35 nm

40 nm

45 nm

50 nm

55 nm

60 nm

65 nm

70 nm

0%1%1%2%2%3%3%4%4%5%5%6%6%7%7%8%8%

7.50%-8.00%

7.00%-7.50%

6.50%-7.00%

6.00%-6.50%

5.50%-6.00%

5.00%-5.50%

4.50%-5.00%

4.00%-4.50%

3.50%-4.00%

3.00%-3.50%

2.50%-3.00%

2.00%-2.50%

1.50%-2.00%

1.00%-1.50%

0.50%-1.00%

0.00%-0.50%

ffLEDLED – Photometer 1 – Photometer 1

10.00

20.00

30.00

40.00

50.00

60.00

70.00

430.00 480.00 530.00 580.00 630.00

We can We can overlay a plot overlay a plot of FWHM vs. of FWHM vs. wavelength wavelength

for some for some modern LEDSmodern LEDS

We can We can overlay a plot overlay a plot of FWHM vs. of FWHM vs. wavelength wavelength

for some for some modern LEDSmodern LEDS

These would These would be measured be measured with <2% fwith <2% fLED.LED.

These would These would be measured be measured with <2% fwith <2% fLED.LED.

These would be measured These would be measured with <1% fwith <1% fLED.LED.

These would be measured These would be measured with <1% fwith <1% fLED.LED.


10

15

20

25

30

35

40

45

50

55

60

65

70

0%1%1%2%2%3%3%4%4%5%5%6%6%7%7%8%8%

7.50%-8.00%

7.00%-7.50%

6.50%-7.00%

6.00%-6.50%

5.50%-6.00%

5.00%-5.50%

4.50%-5.00%

4.00%-4.50%

3.50%-4.00%

3.00%-3.50%

2.50%-3.00%

2.00%-2.50%

1.50%-2.00%

1.00%-1.50%

0.50%-1.00%

0.00%-0.50%

ffLED LED – Photometer 2– Photometer 2

10.00

20.00

30.00

40.00

50.00

60.00

70.00

430.00 480.00 530.00 580.00 630.00

Photometer 2 has <1% fPhotometer 2 has <1% fLEDLED for most LEDs. for most LEDs.Photometer 2 has <1% fPhotometer 2 has <1% fLEDLED for most LEDs. for most LEDs.

But offers no significant But offers no significant improvement for these improvement for these

LEDs.LEDs.

But offers no significant But offers no significant improvement for these improvement for these

LEDs.LEDs.


10

15

20

25

30

35

40

45

50

55

60

65

70

0.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%4.00%4.50%5.00%5.50%6.00%6.50%7.00%7.50%8.00%

7.50%-8.00%

7.00%-7.50%

6.50%-7.00%

6.00%-6.50%

5.50%-6.00%

5.00%-5.50%

4.50%-5.00%

4.00%-4.50%

3.50%-4.00%

3.00%-3.50%

2.50%-3.00%

2.00%-2.50%

1.50%-2.00%

1.00%-1.50%

0.50%-1.00%

0.00%-0.50%


10.00

20.00

30.00

40.00

50.00

60.00

70.00

430.00 480.00 530.00 580.00 630.00

Photometer 3 also has a wide range Photometer 3 also has a wide range of <1% fof <1% fLED.LED.

Photometer 3 also has a wide range Photometer 3 also has a wide range of <1% fof <1% fLED.LED.

But up to 7% fBut up to 7% fLEDLED

for these LEDs.for these LEDs.But up to 7% fBut up to 7% fLEDLED

for these LEDs.for these LEDs.

CIE 2CIE 2ndnd Expert Symposium on LEDs Expert Symposium on LEDs430 440 450 460 470 480 490 500 510 520 530 540 550

10

15

20

25

30

35

40

45

50

55

60

65

700.075-0.08

0.07-0.075

0.065-0.07

0.06-0.065

0.055-0.06

0.05-0.055

0.045-0.05

0.04-0.045

0.035-0.04

0.03-0.035

0.025-0.03

0.02-0.025

0.015-0.02

0.01-0.015

0.005-0.01

0-0.005


10.00

20.00

30.00

40.00

50.00

60.00

70.00

430.00 480.00 530.00 580.00 630.00

Photometer 4 data has a limited Photometer 4 data has a limited wavelength range, but <1% fwavelength range, but <1% fLED LED

extends further into the blue extends further into the blue region than the others.region than the others.

Photometer 4 data has a limited Photometer 4 data has a limited wavelength range, but <1% fwavelength range, but <1% fLED LED

extends further into the blue extends further into the blue region than the others.region than the others.

And has fAnd has fLEDLED<3% <3%

even for these LEDs.even for these LEDs.And has fAnd has fLEDLED<3% <3%

even for these LEDs.even for these LEDs.


ffLEDLEDLED batches

10

15

20

25

30

35

40

45

50

400 450 500 550 600 650 700

Peak Wavelength [nm]

FW

HM

[n

m]

To test the validity and To test the validity and usefulness of fusefulness of fLEDLED, ,

several batches of several batches of LEDs were measured.LEDs were measured.

To test the validity and To test the validity and usefulness of fusefulness of fLEDLED, ,

several batches of several batches of LEDs were measured.LEDs were measured.

Each batch included Each batch included similar LEDs in terms similar LEDs in terms of peak and FWHM, of peak and FWHM,

regardless of regardless of manufacturermanufacturer

Each batch included Each batch included similar LEDs in terms similar LEDs in terms of peak and FWHM, of peak and FWHM,

regardless of regardless of manufacturermanufacturer

The “central” LED in The “central” LED in each batch was used to each batch was used to

calibrate the calibrate the photometers for the photometers for the measurement of all measurement of all

other LEDs in the batch.other LEDs in the batch.

The “central” LED in The “central” LED in each batch was used to each batch was used to

calibrate the calibrate the photometers for the photometers for the measurement of all measurement of all

other LEDs in the batch.other LEDs in the batch.

Calibration Calibration LEDs shown LEDs shown

in blackin black

Calibration Calibration LEDs shown LEDs shown

in blackin black


ffLEDLEDLED batches

10

15

20

25

30

35

40

45

50

400 450 500 550 600 650 700

Peak Wavelength [nm]

FW

HM

[n

m]

The spectra of each of The spectra of each of these LEDs is known, so these LEDs is known, so

we can calculate the we can calculate the error in measurement error in measurement

and hence the standard and hence the standard deviation for each batchdeviation for each batch

The spectra of each of The spectra of each of these LEDs is known, so these LEDs is known, so

we can calculate the we can calculate the error in measurement error in measurement

and hence the standard and hence the standard deviation for each batchdeviation for each batch

But the But the extent is extent is

not not 5 nm 5 nm like flike fLED.LED.

But the But the extent is extent is

not not 5 nm 5 nm like flike fLED.LED.

The smaller the spread in The smaller the spread in wavelengths, the lower the wavelengths, the lower the batch error. We can scale batch error. We can scale

the errors to a the errors to a 5 nm 5 nm region to compare directly region to compare directly

with fwith fLED.LED.

The smaller the spread in The smaller the spread in wavelengths, the lower the wavelengths, the lower the batch error. We can scale batch error. We can scale

the errors to a the errors to a 5 nm 5 nm region to compare directly region to compare directly

with fwith fLED.LED.


ffLEDLEDCorrelation of Results for real LEDs to fLED

ALL photometers and ALL LED batches

0%

1%

2%

3%

4%

5%

0% 1% 2% 3% 4% 5%

fLED

Sta

nd

ard

De

via

tio

n o

f E

rro

rs i

n r

ea

l L

ED

ba

tch

es

[sc

ale

d t

o ±

5 n

m r

eg

ion

]

The blue line The blue line represents represents

equivalence.equivalence.

The blue line The blue line represents represents

equivalence.equivalence.


ffLEDLED

ffLEDLED and and LEDs: and and LEDs:

ffLEDLED is specific to LED measurement. is specific to LED measurement. ffLEDLED is based on variations in spectral is based on variations in spectral

mismatch factors.mismatch factors. ffLEDLED reflects actual measurement procedures. reflects actual measurement procedures.

ffLEDLED agrees with results. agrees with results. ffLEDLED applies to all LEDs and photometers applies to all LEDs and photometers

investigated and is robust enough for future investigated and is robust enough for future developments.developments.

ffLEDLED and and LEDs: and and LEDs:

ffLEDLED is specific to LED measurement. is specific to LED measurement. ffLEDLED is based on variations in spectral is based on variations in spectral

mismatch factors.mismatch factors. ffLEDLED reflects actual measurement procedures. reflects actual measurement procedures.

ffLEDLED agrees with results. agrees with results. ffLEDLED applies to all LEDs and photometers applies to all LEDs and photometers

investigated and is robust enough for future investigated and is robust enough for future developments.developments.


ffLEDLED

ffLEDLED and manufacturers: and manufacturers:

ffLEDLED helps in design of better photometers. helps in design of better photometers.

ffLEDLED does not require any more measurements does not require any more measurements than is currently done for calculation of fthan is currently done for calculation of f11’.’.

ffLEDLED can be calculated from limited range data can be calculated from limited range data – it does not require the full visible range.– it does not require the full visible range.

ffLEDLED should be calculated from data at 1 nm or should be calculated from data at 1 nm or smaller intervals.smaller intervals.

ffLEDLED and manufacturers: and manufacturers:

ffLEDLED helps in design of better photometers. helps in design of better photometers.

ffLEDLED does not require any more measurements does not require any more measurements than is currently done for calculation of fthan is currently done for calculation of f11’.’.

ffLEDLED can be calculated from limited range data can be calculated from limited range data – it does not require the full visible range.– it does not require the full visible range.

ffLEDLED should be calculated from data at 1 nm or should be calculated from data at 1 nm or smaller intervals.smaller intervals.


ffLEDLED

ffLEDLED and users: and users:

ffLEDLED provides a much better selection criterion than f provides a much better selection criterion than f11’.’.

ffLEDLED is a property of the photometer, eliminating is a property of the photometer, eliminating

confusion on calibration requirements.confusion on calibration requirements. ffLEDLED allows for optimization of photometer selection allows for optimization of photometer selection

across all the user’s LED requirements.across all the user’s LED requirements.

ffLEDLED gives an indication of errors in measurement. gives an indication of errors in measurement. Advances in quality of photometers and better Advances in quality of photometers and better

selection will reduce uncertainties in measurement.selection will reduce uncertainties in measurement.

ffLEDLED and users: and users:

ffLEDLED provides a much better selection criterion than f provides a much better selection criterion than f11’.’.

ffLEDLED is a property of the photometer, eliminating is a property of the photometer, eliminating

confusion on calibration requirements.confusion on calibration requirements. ffLEDLED allows for optimization of photometer selection allows for optimization of photometer selection

across all the user’s LED requirements.across all the user’s LED requirements.

ffLEDLED gives an indication of errors in measurement. gives an indication of errors in measurement. Advances in quality of photometers and better Advances in quality of photometers and better

selection will reduce uncertainties in measurement.selection will reduce uncertainties in measurement.


AcknowledgementsAcknowledgements

Thanks to NIST and Lumileds.Thanks to NIST and Lumileds. For the great quantity and quality of data provided For the great quantity and quality of data provided

by them.by them.

Thanks to all the members of CIE TC2-45 and Thanks to all the members of CIE TC2-45 and

TC2-46.TC2-46. For their useful input and discussions.For their useful input and discussions.

Special thanks to Yoshi Ohno, NIST.Special thanks to Yoshi Ohno, NIST. For all his help.For all his help.

Thanks to NIST and Lumileds.Thanks to NIST and Lumileds. For the great quantity and quality of data provided For the great quantity and quality of data provided

by them.by them.

Thanks to all the members of CIE TC2-45 and Thanks to all the members of CIE TC2-45 and

TC2-46.TC2-46. For their useful input and discussions.For their useful input and discussions.

Special thanks to Yoshi Ohno, NIST.Special thanks to Yoshi Ohno, NIST. For all his help.For all his help.

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Richard Young Richard Young Optronic Laboratories Kathleen Muray Kathleen Muray INPHORA Carolyn Jones Carolyn Jones CJ Enterprises